The NPR in my current game is hampered on exploration because it has only 2 naval shipyards one at 3k tons and the other at 1k tons.
It does have a couple of survey ships with jump engines and at least one jump destroyer (all of which are too large to have been built in the SY btw

) but it has not expanded at any noticeable rate in a few years of game time. Because it has no commercial yards it can not build jump gates which is another reason it is lacking in expansion.
Might I suggest two things:
1. If possible, on NPR creation, create the shipyards first and then using the capacity of the shipyard design the ships and create the first couple of fleets worth from those designs.
2. Maybe cheat a little for the NPRs and make sure they have at least 1 commercial SY of a decent size at the start, otherwise they are gimped!